The company previously offered $US30 ($A43) per share when it first went directly to Warner stakeholders with its all-cash, hostile bid in December - just days after Warner struck a deal to sell its studio and streaming business to Netflix for $US27.75 ($A39.40) per share.
Beyond upping its proposed purchase price, Warner said on Tuesday afternoon, local time, that Paramount had increased its regulatory termination fee to $US7 billion ($A9.9 billion).
Paramount also agreed to move up a previously promised "ticking fee" payable to shareholders if its deal doesn't go through now by the end of September - amounting to 25 cents per share, or a total of $US650 million ($A923 million).
After briefly reopening talks with Paramount, Warner earlier confirmed it had received a revised offer and was reviewing it.
When announcing the increased price, Warner said Paramount's revised proposal "could reasonably be expected to lead to" a superior offer as defined under its current agreement with Netflix - but the company's board has still not actually determined whether Paramount's offer is better than Netflix's.
A Netflix spokesperson declined to comment.
A Warner Bros Discovery buyout would reshape Hollywood and the wider media landscape - bringing HBO Max, cult-favourite titles like Harry Potter and, depending on who wins the Netflix v Paramount tug-of-war, potentially even CNN under a new roof.
Paramount wants to acquire Warner Bros in its entirety - including networks like CNN and Discovery.
But Netflix only wants to buy Warner's studio and streaming business. Warner's board has repeatedly backed this deal, and on Tuesday maintained that its agreement with Netflix still stands.
If Warner's board later deems Paramount's offer to be superior, however, Netflix would then have four days to match or revise its proposal. It could also choose to walk away.
Paramount, Warner and Netflix have spent the last couple of months in a heated back-and-forth over who has a stronger deal.
But many lawmakers and entertainment trade groups have sounded the alarm along the way, warning that either buyout of all or parts of Warner's business would only further consolidate power in an industry already run by just a few major players.
Critics say that could result in job losses, less diversity in filmmaking and potentially more headaches for consumers who are facing rising costs of streaming subscriptions as is.
Combined, that raises tremendous antitrust concerns - and a Warner sale could come down to who gets the regulatory greenlight.
The US Department of Justice has already initiated reviews, and other nations are expected to do so.
